Very true on this being better than a lawsuit from the RIAA. Compared to that, this is nothing, so relax a little.
Now, one thing I just thought of that no one has mentioned: Even though its probably very illegal, given the requests so far, I wouldn't put it past the tech department you're dealing with to do it, but I would be worried they might install something on your computer to monitor future downloads. I know it sounds crazy at first, but I'll bet they could hide that in a University terms of use document somewhere or in the stuff you just signed when you gave them the PC. So it might be a good idea to format it anyway when you get it back for that reason. Or I could just be paranoid.
As far as getting your computer back, they will only answer the phone so many times before getting annoyed saying "It'll be done soon...."